Relativistic Quantum Models Research Articles

Realization of Jackiw–Rebbi zero-energy modes at photonic crystal domain walls: Emergence of polarization-indiscriminate surface states

The Jackiw–Rebbi model is a relativistic quantum model credited with the theoretical predictions of zero-energy bound states and charge fractionalization prior to the discovery of topological insulators and the fractional quantum Hall effect. In this work, we demonstrate a photonic equivalent of the Jackiw–Rebbi model by resorting to photonic crystal band structure engineering. Specifically, our photonic realization employs two spatial inversion symmetric binary photonic crystals exhibiting complementary signs of differential effective mass parameter (δm) for their second bandgaps. Their concatenation manifests a step discontinuity in the spatial profile of the effective mass parameter, forming a domain wall at the photonic crystal interface. Upon analyzing the reflectance spectra of the concatenated photonic crystal structure, we find a midgap surface state localized at this domain wall. Furthermore, much in agreement with the Jackiw–Rebbi zero-energy solution, the materialized photonic surface state also exhibits a zero-energy character in a differential energy space corresponding to the δm parameter, which has been quantified experimentally. Crucially, the conceived zero-energy mode amounts to the observation of a peculiar surface state with polarization-indiscriminate dispersion that can help realize all-angle polarization neutral optics.

Geometry of a Relativistic Quantum Chaos: New approach to dynamics of quantum systems in electromagnetic field and some applications

In the paper we present development of a new relativistic chaos-geometric and quantum-dynamic approach to solve problems of complete modelling relativistic chaotic dynamics of atoms in an electromagnetic field. As usually the approach consistently includes a number of new relativistic quantum models and a number of new or improved methods of analysis (correlation integral, fractal analysis, algorithms, average mutual information, false nearest neighbors, Lyapunov exponents, surrogate data, non-linear prediction, spectral methods, etc.) For the first time we present the corresponding atomic ionization quantitative data for some atoms in a microwave external field.

Геометрия релятивистского квантового хаоса: Новый подход к динамике квантовых систем в электромагнитном поле и единообразие и очарование хаоса

Work is devoted to the development of the theoretical foundations of the universal new relativistic chaos-geometric and quantum-dynamic approach that consistently includes a number of new relativistic quantum models and a number of new or improved methods of analysis (correlation integral, fractal analysis, algorithms, average mutual information, false nearest neighbors, Lyapunov exponents, surrogate data, non-linear prediction, spectral methods, etc.) to solve problems of complete modelling relativistic chaotic dynamics in an electromagnetic field. For a number of atomic systems there are firstly discovered availability of a relativistic quantum chaos and obtained the corresponding quantitative data on the chaos characteristics.

Stability of Covariant Relativistic Quantum Theory

In this paper we study the relativistic quantum-mechanical interpretation of the solution of the inhomogeneous Euclidean Bethe-Salpeter equation. Our goal is to determine conditions on the input to the Euclidean Bethe-Salpeter equation so the solution can be used to construct a model Hilbert space and a dynamical unitary representation of the Poincaré group. We prove three theorems that relate the stability of this construction to properties of the kernel and driving term of the Bethe-Salpeter equation. The most interesting result is that the positivity of the Hilbert space norm in the non-interacting theory is not stable with respect to Euclidean covariant perturbations defined by Bethe-Salpeter kernels. The long-term goal of this work is to understand which model Euclidean Green functions preserve the underlying relativistic quantum theory of the original field theory. Understanding the constraints imposed on the Green functions by the existence of an underlying relativistic quantum theory is an important consideration for formulating field-theory motivated relativistic quantum models.

Large-N theory from the axiomatic point of view

The state space and observables for the leading order of the large-N theory are constructed. The obtained model (“theory of infinite number of fields”) is shown to obey Wightman-type axioms (including invariance under boost transformations). The considered class of exactly solvable relativistic quantum models involves good examples of theories containing such difficulties as volume divergences associated with the Haag theorem, Stueckelberg divergences, and infinite renormalization of the wave function.

A relativistic quark model of mesons

We propose a relativistic quantum model to describe mesons comprising a quark and an antiquark with arbitrary masses. The Dirac equations describe the quarks, and the rigid string approximation accounts for the gluon field contribution. The model fits the meson spectra well and determines the masses of the s-, c-, and b-quarks and the relativistic wave functions of compound mesons.

Relativistic quantum model of confinement and the current quark masses

We consider a relativistic quantum model of confined massive spinning quarks and antiquarks which describes leading Regge trajectories of mesons. The quarks are described by the Dirac equations and the gluon contribution is approximated by the Nambu-Goto straight-line string. The string tension and the current quark masses are the main parameters of the model. Additional parameters are phenomenological constants which approximate nonstring short-range contributions. Comparison of the measured meson masses with the model predictions allows one to determine the current quark masses (in MeV) to be $m_s = 227 \pm 5,~ m_c = 1440 \pm 10,~ m_b = 4715 \pm 20$. The chiral $SU_3$ model[23] makes it possible to estimate from here the $u$- and $d$-quark masses to be $m_u = 6.2 \pm 0.2$~ Mev and $m_d = 11.1 \pm 0.4$ Mev.

Growing Regge trajectories in relativistic string models

A relativistic quantum model is suggested in which the Regge trajectories can grow faster than linearly. The model is a rigid string with a Lagrangian given by an exponential function of the string world-sheet curvature. Exactly solvable generalizations of the model are considered.

Quantum relativity theory and quantum space-time

A quantum relativity theory formulated in terms of Davis' quantum relativity principle is outlined. The first task in this theory as in classical relativity theory is to model space-time, the arena of natural processes. It is shown that the quantum space-time models of Banai introduced in another paper is formulated in terms of Davis' quantum relativity. The recently proposed classical relativistic quantum theory of Prugovecki and his corresponding classical relativistic quantum model of space-time open the way to introduce, in a consistent way, the quantum space-time model (the quantum substitute of Minkowski space) of Banai proposed in the paper mentioned. The goal of quantum mechanics of quantum relativistic particles living in this model of space-time is to predict the rest mass system properties of classically relativistic (massive) quantum particles (“elementary particles”). The main new aspect of this quantum mechanics is that provides a true mass eigenvalue problem, and that the excited mass states of quantum relativistic particles can be interpreted as elementary particles. The question of field theory over quantum relativistic model of space-time is also discussed. Finally it is suggested that “quarks” should be considered as quantum relativistic particles.

Conductive string: A relativistic quantum model of particles with internal structure

Conductive string: A relativistic quantum model of particles with internal structure